In order to find and classify these solutions, several algebraic structures were provided. In 2007 Rump [1]} introduced left braces, algebraic structures that include Jacobson radical rings. Left braces determine set-theoretic solutions, and conversely, given a set-theoretic solution \((X,r)\) , one can associate a left brace \(\mathcal {G}(X,r)\) . As showed in several recent papers, left braces can be used to take informations on set-theoretic solutions such as retractability, indecomposability and simplicity (see for example [2]}, [3]}, [4]}, [5]}, [6]},  and related references).
